Sure, Archer started out in "Broken Bow" (even the prologue with li'l Jonny) resentful of Vulcans, including T'Pol, because he blamed them for holding back his dad, and humanity. (Which they did - Soval told Forrest that.) BUT by the end of the episode, Archer had saved T'Pol's life, let her remain acting Captain, apologized to her for his preconceived notions regarding her, and asked her to stay on board as Science Officer. By "Shadows of P'Jem" he fights tooth and nail to keep T'Pol on Enterprise. By "Fusion" he literally fights Tolaris in order to get him tossed off the ship, to keep T'Pol safe - and he's totally pissed that T'Pol won't press charges and get justice. By that last scene in "Fusion," and his concern for her, and his guilt for putting T'Pol and Tolaris together, I see no animosity against her anymore. By "Acquisition" their partnership has progressed to the point where she teases him when he's cuffed and she has the key. By "Shockwave II" after T'Pol's speech convinces the VHC not to recall Enterprise, Archer wants to show his gratitude so much he wakes her to tell her she "put it over the top."
No, it didn't happen immediately, it took half a season. But his struggle to widen his horizons regarding T'Pol was the same metaphor for the struggle of humans vs Vulcans, and Tucker vs T'Pol, as they learned and grew.
After "Shockwave II" Archer and T'Pol were, to my view, committed shipmates and friends. In "The Expanse" he's concerned when she decides to resign the VHC to stay with ENT. At the end of "Impulse" he refuses to leave her behind. And Archer's huge distrust of Vulcans-- actually, the VHC-- lingered even after he accepted T'Pol, and it ended up being totally true - the spy station on P'Jem, plotting for war against Andoria, V'Las's duplicity, the sacking of Soval - and the VHC's terrible treatment of T'Pol herself.
Sure, the showrunners wanted us to sympathize with Archer and Tucker (they were the leads, etc)... but in-universe, the setup seems to be because they were human, and the Vulcans were alien. Archer's friendship with T'Pol, and Phlox too for that matter, was about their value as shipmates, then as people. The whole point of science fiction is to look at humanity, with all its flaws and limitations, and hopefully see humans accept, even embrace, those who are different. ENT did that all the way to the end, with Paxton's xenophobia.